Stability and instability of standing waves for 1-dimensional nonlinear Schrödinger equation with multiple-power nonlinearity. (English) Zbl 1180.35483

Maeda, Masaya

Kodai Math. J. 31, No. 2, 263-271 (2008).

From the author’s abstract: We consider the stability and instability of standing waves for the following nonlinear Schrödinger equation: \[ iu_t+u_{xx}+f(u)=0,\quad t\geq 0,\;x\in \mathbb{R}, \] where \(f(u)=\sum^m_{j=1}a_j| u|^{p_j-1}u\) with \(a_j\in\mathbb{R}\) and \(1<p_1<\cdots<p_m<\infty\).

Reviewer: A. D. Osborne (Keele)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35B35	Stability in context of PDEs